It seems that, as of late, people's IP addresses that are on major ISPs (cable Internet, or DSL) are essentially static for long periods of time. Is this a fair assumption?
How does this change in the mobile environment?
Are IP addresses more dynamic when browsing on mobile phones and tablets that are using mobile networks?
They may or may not be. In the days of dialup, people frequently disconnected - every time you dialed in, you would request a new IP, and the server may or may not hand the same one out to you. It was much easier for an ISP to change IPs then. They also did this to save IPs - if you have 1000 dialup users, but only 100 connect at the same time, then you only need 100 IPs. Each time a user disconnects, they free up an IP which gets used by the next user to connect.
Today, many more users connect over cable or DSL, and their modems are connected 24/7. While it can be done, changing these IPs while devices are connected through the modem is much more problematic and it's easier to just let the modem continue using the same IP when the DHCP reservation expires since changing IPs isn't going to let you "save" IPs - the modem still needs one. Personal experience has shown me that these IPs still tend to change when the modem disconnects and reconnects to the network, but for many people, that only happens during a power or network outage, instead of when they get up from the computer.
As to cellular networks, they hold true to the same rules (IPs are prone to changing when the phone disconnects and reconnects to the cellular data network), and the devices disconnect much more frequently than cable or DSL modems (battery dies, loss of signal, phone sleeps the modem to save power, phone switches to WiFi and disconnects from cellular data, etc.)
This may all change with IPv6. Dynamic IPs and NAT (network address translation) are only necessary because there are far more connected network devices than there are IPv4 IPs (think about the dialup situation I mentioned: 1000 devices, 100 IPs). We actually ran out of IPv4 IPs a while back, and so address space is getting incredibly tight as more and more devices are becoming connected 24/7. IPv6 significantly increases the number of IPs we have available - enough for every person on the planet to have 48,000 trillion trillion addresses all to their own. This will likely bring us into a world where every device has its own static IP.
In my experience, I've only seen IP changes on broadband once every year or two, so I've treated it as essentially static. It may depend on whether the router is on 24/7.
Mobile is another question. I haven't been keeping track of my cellular IP, but my phone also hops between different WiFi networks and cellular data all day. So while my IP might be fixed on the cellular side, the IP that I'm actually using to access the internet is changing all the time.
I don't know about the mobile environment, but I run a Dynsdns out of my home and I find it has to update itself every 2-3 days with a new IP. But then it may also depend on other factors such as ISP, neighborhood saturation, demand, etc.
